Global Optimization Procedure Research Articles

Reliability-based optimization of supported pendulum TMDs’ nonlinear track shape using Padé approximants

Supported Pendulum Tuned Mass Dampers (PTMDs) are vibration absorbers whose mass is constrained to oscillate along a curved path, enabling to use gravity as a restoring force. Through a proper track shape selection, they can adapt to the so-called Nonlinear Energy Sinks (NES) concept, consolidated for spring–mass–damper TMDs. Accordingly, NESs are recognized for their ability to resonate in a wide range of frequencies due to their nonlinear nature, becoming more effective when variations on the host structure’s natural frequencies occur. However, regardless of the recent advances in the last few years, gaps remain to be explored in the track shape optimization of supported PTMDs. For instance, a comprehensive literature review shows that Reliability-Based Design Optimization (RBDO) studies to determine the track shape of supported PTMDs cannot be found to the best of the author’s knowledge. Within this context, this paper proposes an original RBDO approach to define the track shape of supported PTMDs in buildings subjected to seismic excitation. For this purpose, a generic rational function with an arbitrary curvature, determined from the Padé approximation of the circle equation, is constructed to allow the PTMD’s path shape search. This procedure allows optimizing fewer parameters than required in Taylor series expansions while providing a wider range of alternatives for numerical optimization. Finally, an active-learning Kriging-based Efficient Global Optimization (EGO) procedure is employed to find the optimum solutions with few objective function evaluations. The application case consists of a typical soft story building subjected to seismic loadings. The optimal track differs from the circle equation, with a higher slope for moderate displacements.

Two-Age-Structured COVID-19 Epidemic Model: Estimation of Virulence Parameters through New Data Incorporation

The COVID-19 epidemic has required countries to implement different containment strategies to limit its spread, like strict or weakened national lockdown rules and the application of age-stratified vaccine prioritization strategies. These interventions have in turn modified the age-dependent patterns of social contacts. In our recent paper, starting from the available age-structured real data at the national level, we identified, for the Italian case, specific virulence parameters for a two-age-structured COVID-19 epidemic compartmental model (under 60, and 60 years and over) in six different diseases transmission scenarios under concurrently adopted feedback interventions. An interpretation of how each external scenario modifies the age-dependent patterns of social contacts and the spread of COVID-19 disease has been accordingly provided. In this paper, which can be viewed as a sequel to the previous one, we mainly apply the same general methodology therein (involving the same dynamic model) to new data covering the three subsequent additional scenarios: (i) a mitigated coordinated intermittent regional action in conjunction with the II vaccination phase; (ii) a super-attenuated coordinated intermittent regional action in conjunction with the II vaccination phase; and (iii) a last step towards normality in conjunction with the start of the III vaccination phase. As a new contribution, we show how meaningful updated information can be drawn out, once the identification of virulence parameters, characterizing the two age groups within the latest three different phases, is successfully carried out. Nevertheless, differently from our previous paper, the global optimization procedure is carried out here with the number of susceptible individuals in each scenario being left free to change, to account for reinfection and immunity due to vaccination. Not only do the slightly different estimates we obtain for the previous scenarios not impact any of the previous considerations (and thus illustrate the robustness of the procedure), but also, and mainly, the new results provide a meaningful picture of the evolution of social behaviors, along with the goodness of strategic interventions.

High-efficacy global optimization of antenna structures by means of simplex-based predictors

Design of modern antenna systems has become highly dependent on computational tools, especially full-wave electromagnetic (EM) simulation models. EM analysis is capable of yielding accurate representation of antenna characteristics at the expense of considerable evaluation time. Consequently, execution of simulation-driven design procedures (optimization, statistical analysis, multi-criterial design) is severely hindered by the accumulated cost of multiple antenna evaluations. This problem is especially pronounced in the case of global search, frequently performed using nature-inspired algorithms, known for poor computational efficiency. At the same time, global optimization is often required, either due to multimodality of the design task or the lack of sufficiently good starting point. A workaround is to combine metaheuristics with surrogate modeling methods, yet a construction of reliable metamodels over broad ranges of antenna parameters is challenging. This work introduces a novel procedure for global optimization of antenna structures. Our methodology involves a simplex-based automated search performed at the level of approximated operating and performance figures of the structure at hand. The presented approach capitalizes on weakly-nonlinear dependence between the operating figures and antenna geometry parameters, as well as computationally cheap design updates, only requiring a single EM analysis per iteration. Formal convergence of the algorithm is guaranteed by implementing the automated decision-making procedure for reducing the simplex size upon detecting the lack of objective function improvement. The global optimization stage is succeeded by gradient-based parameter refinement. The proposed procedure has been validated using four microstrip antenna structures. Multiple independent runs and statistical analysis of the results have been carried out in order to corroborate global search capability. Satisfactory outcome obtained for all instances, and low average computational cost of only 120 EM antenna simulations, demonstrate superior efficacy of our algorithm, also in comparison with both local optimizers and nature-inspired procedures.

Advanced Bio-Inspired computing paradigm for nonlinear smoking model

Smoking has emerged as one of the leading global factors that is the source of health issues. It damages almost all of the body's organs. It damages various muscles and causes lung cancer. Additionally, it causes ulcers, pulmonary disease, and vascular deterioration. Except for the financial benefit to tobacco companies, manufacturers, and marketing companies, smoking has no advantages. Due to these factors, the present study exploited a feed forward neural networking based global optimization procedure with a local scheme to solve a mathematical model of smoking. A genetic based algorithm and sequential quadratic programming (GA-SQP) are utilized as hybridized global and local strategies. The model is categorized into five classes: potential smokers, occasional smokers, smokers, temporary quit, and permanent quit smokers. An objective optimization function is constructed to minimize the mean square error using the designed smoking model in form of feed forward neural networking. The comparative evaluation of hybrid GA-SQP and Adam numerical scheme is also assessed to authenticate the precision and correctness of the solution of the smoking model. The robustness, perfection, and convergence stability of GA-SQP are verified by establishing various statistical performance indicators. The quantitative analysis provides the minimum, mean, and semi-inter quartile range values for absolute errors up to 6 to 13 decimal places, demonstrating the worthiness and precision of the proposed GA-SQP.

Performance-based optimization of nonlinear Friction-Folded PTMDs of structures subjected to stochastic excitation

Alternative Tuned Mass Damper (TMD) configurations have been proposed in the literature for performance improvement and maintenance, mainly modifying their restoring force or dissipation mechanisms. In this context, Folded-Pendulum TMDs (FPTMDs) are appealing for tuning low-frequency structures because they are compact and easy to retune while avoiding sliding mechanisms. In turn, Friction Dampers (FDs) are equally attractive due to their minimal maintenance and easy desired capacity adjustment. Nevertheless, despite recent advances in integrating FDs with PTMDs, a comprehensive literature survey reveals that Reliability-Based Design Optimization (RBDO) studies for PTMDs or Folded-PTMDs with FDs cannot be found to the best of the authors’ knowledge. Hence, the present paper aims at performing an original RBDO of single and multiple Friction-Folded-PTMDs in buildings subjected to stochastic excitation. Unlike the existing optimization studies in this field, a complete nonlinear description (dry friction plus large rotations) is employed because the considered applications involve high-intensity excitations, like wind and seismic loading. Finally, scenarios with multiple absorbers are included due to their associated performance and constructional advantages. Optimal design of multiple Folded-PTMDs with FDs has not yet been addressed, as they increase the optimization problem complexity leading to multimodal and convex objective functions. Accordingly, an active-learning Kriging-based Efficient Global Optimization (EGO) procedure is used, which allows for finding the optimum solutions with only a few objective function evaluations. The application cases to two distinct buildings subject to wind and seismic loadings show that using Friction-FPTMDs allows for obtaining a control strategy with an appropriate performance while ensuring practical advantages over classical TMDs.

A novel method for the globally optimal design of fixed bed catalytic reactors

Fixed bed reactors are usually designed using simulation approaches by trying different dimensions as well as operating conditions followed by verification if the desired conversion is achieved. This trial and verification procedure does not guarantee optimality, just a feasible and reasonably good design (depending on the expertise of the designer). Cost minimization or profit maximization using optimization procedures is more rigorous, but it has been rarely employed. The methods usually employed in the literature for solving this design problem present limitations. In this article, we solve the design problem of fixed bed catalytic reactors globally. We use Partial Set Trimming followed by Smart Enumeration, a recently developed rigorous global optimization procedure. The reactor investigated is composed of a tube bundle, filled with a catalyst, inside a shell containing boiling water. We compare the performance of the proposed approach with the use of metaheuristics-based tools, which do not guarantee optimality.

Calibration of Watershed Conceptual Models Using Local and Global ptimization

Many issues related to water resources require the solution of optimization problems. Optimization problems can be quite difficult such as the calibration of many conceptual watershed models. Conceptual watershed models are formulated using empirical relationships between hydrological variables observed in nature or field experiments .The success of automatic calibration depends mainly on the choice of optimization method. Most early attempts to calibrate watershed models have been based on local-search optimization methods. Local optimization methods are not designed to handle the presence of multiple regions of attraction, multi-local optima, insensitivities and parameter interdependencies, and other problems encountered in the calibration of watersheds models. It is therefore imperative that global optimization procedures that are capable of dealing with these various difficulties be employed. In this study, one local search optimization method and one global search method are used to calibrate the parameters a simple tenparameter rainfall-runoff model. The local search method is the well-known Rosenbrock's direct search method; the global search method is the newly developed Shuffled Complex Evolution (SCE) method . The results revealed that Shuffle Complex Evolution optimization method is more superior to Rosenbrok’s direct search method. The results confirmed the finding of many watershed modellers about the dependency of Rosenbrock’s method on the choice of initial search points. It further adds that Rosenbrock’s method is only effective when the initial search points are taken within 5 % or less from the true optimum parameter set. The results indicate that a proper choice of optimization methods can enhance the possibility of obtaining unique and conceptually realistic parameter estimate.

Global optimisation procedures for solving systems of Hölder equations-inequations

Global optimisation procedures for solving systems of Hölder equations-inequations

Global optimisation procedures for solving systems of Hölder equations-inequations

Global optimisation procedures for solving systems of Hölder equations-inequations

DEVELOPMENT OF OPTICAL SYSTEMS OF 16-LENS ORTHOSCOPIC TELEPHOTO LENSES

In this work, the possibilities of creating multi-lens optical systems of telephoto lenses with a fixed focal length and high image quality with the help of a computer have been experimentally investigated. The effectiveness of the automated procedure for creating new optical systems of orthoscopic telephoto lenses was repeatedly examined. The design procedure utilizes a modified version of the modern stochastic global optimization algorithm. In particular, we carried out the aberration synthesis of several optical systems of 16-lens orthoscopic telephoto lenses having the effective focal length of 300 mm and a F-number equal to 2.8, and designed to work in the visible spectral range with 35-mm full-frame image matrix detectors. Multiple computer simulations of the design process have shown that the global optimization procedure with a total number of variables of around 90 requires significant computing power. Specifically, when running on the Intel Core i9-9900K processor in multi-threaded mode and optimizing the values of the modulation transfer functions, the design procedure can exceed 50 hours. The maximum value of the relative distortion of synthesized variants of telephoto lenses does not exceed 0.017%. In all considered cases, the values of polychromatic modulation transfer functions for a spatial frequency of 30 lines/mm are not smaller than 0.5 over the entire image field. The design results obtained for the specified telephoto lenses confirm the effectiveness of the proposed approach and the practical possibility of achieving high-quality correction of aberrations in the above-mentioned multi-lens telephoto systems even without the use of fluorite (calcium fluoride).

Using a Fully Fractional Generalised Maxwell Model for Describing the Time Dependent Sinusoidal Creep of a Dielectric Elastomer Actuator

Actuators made of dielectric elastomers are used in soft robotics for a variety of applications. However, due to their mechanical properties, they exhibit viscoelastic behaviour, especially in the initial phase of their performance, which can be observed in the first cycles of dynamic excitation. A fully fractional generalised Maxwell model was derived and used for the first time to capture the viscoelastic effect of dielectric elastomer actuators. The Laplace transform was used to derive the fully fractional generalised Maxwell model. The Laplace transform has proven to be very useful and practical in deriving fractional viscoelastic constitutive models. Using the global optimisation procedure called Pattern Search, the optimal parameters, as well as the number of branches of the fully fractional generalised Maxwell model, were derived from the experimental results. For the fully fractional generalised Maxwell model, the optimal number of branches was determined considering the derivation order of each element of the branch. The derived model can readily be implemented in the simulation of a dielectric elastomer actuator control, and can also easily be used for different viscoelastic materials.

A memetic procedure for global multi-objective optimization

In this paper we consider multi-objective optimization problems over a box. Several computational approaches to solve these problems have been proposed in the literature, that broadly fall into two main classes: evolutionary methods, which are usually very good at exploring the feasible region and retrieving good solutions even in the nonconvex case, and descent methods, which excel in efficiently approximating good quality solutions. In this paper, first we confirm, through numerical experiments, the advantages and disadvantages of these approaches. Then we propose a new method which combines the good features of both. The resulting algorithm, which we call Non-dominated Sorting Memetic Algorithm, besides enjoying interesting theoretical properties, excels in all of the numerical tests we performed on several, widely employed, test functions.

Analysis and Optimization of Organic Tandem Solar Cells by Full Opto-Electronic Simulation

This paper reports on the analysis and optimization of high-efficiency organic tandem solar cells via full opto-electronic device simulation on continuum level and using a hopping model for the explicit description of the charge recombination junction. Inclusion of the electrical sub-cell interconnection allows for a rigorous assessment of the impact of the internal charge distribution and associated built-in fields as well as quasi-Fermi level profiles on the measured device characteristics. It enables the direct evaluation of the external quantum efficiency in a simulation that follows closely the measurement protocol, and sheds light on complications related to the dependence of the band profile on the illumination conditions. The study also points at fingerprints of insufficient junction quality in the electrical characteristics of the tandem device. After studying the impact of key electrical parameters such as, carrier mobility, lifetime and interface hopping rate, onto the device characteristics, the latter are optimized not only optically, but also electronically, adding in both cases an increasing number of layers to the parameters of the global optimization procedure. An improvement of 2% absolute power conversion efficiency by using the full opto-electronic optimization as compared to optical optimization only is found.

Data-Driven Self-Optimizing Control With Parametric Programing Based Constraint Handling

AbstractSelf-optimizing control (SOC) aims to achieve near-optimal operation regardless of variation in disturbances. For constrained operation, the model-based SOC has been solved as an explicit model predictive control (MPC) problem, where the changes in active constraint sets under large variations in disturbance inputs can be determined via parametric programing. For constrained SOC design with historical data only, this paper presents an extended work for a data-driven method that Zhao et al. proposed (2022 “Global Self-Optimizing Control With Data-Driven Optimal Selection of Controlled Variables With Application to Chiller Plant”, ASME J. Dyn. Sys., Meas., Control., 144(2), p. 021008.) for obtaining global SOC solution. While this work remains to adopt the Koopman subspace model that has been used, the SOC-associated constrained optimization problem is solved by applying the multiparameter quadratic programing technique. The solutions consist of piecewise-affine control laws and active constraint sets that are determined via partitions of the disturbance space. The proposed approach is illustrated with a Modelica simulation model of a chilled-water plant, where minimizing the total power consumption is the economic objective. The results show that the proposed method yields the total power very close to that by an offline genetic algorithm-based global optimization procedure, and substantially better than a best-practice rule-based control strategy. The degree of constraint violations under high cooling load is also smaller with the solution of constrained SOC.

BSPASS: A Beam Search-Based Phase Association and Source Scanning Earthquake Location Method

AbstractWe propose a novel phase association and source scanning method by incorporating the norm-grid search and a beam search technique together to associate seismic phases, and to determine the accurate location of a particular event simultaneously. The method is called the beam search-based phase association and source scanning (BSPASS). Using synthetic travel times for two seismic networks with different station spacings, we examine the practicability and accuracy of the BSPASS method. The results show that BSPASS could constrain event location with high precisions, if the standard deviation of travel-time errors is less than 0.4 s. The method works well even for those earthquakes located at the network boundary. We applied the BSPASS method to the beginning day of the 2018 Purcell mountains earthquake swarm. Two times more events are detected automatically, and similar spatiotemporal distribution of these earthquakes is recognized by our method compared to the U.S. Geological Survey catalog. We also investigate the flexibility and robustness of the BSPASS method by adding Gaussian noises to phase arrivals. With the increasing of noise levels, the location errors grow accordingly. Based on our tests, we suggest that there might be an upper limit of phase picking errors for a particular source array configuration, for example, 0.4 s in this study, above which the global optimization procedure fails to resolve a better source location under the constraint of travel-time residuals than that of the norm-grid searching.

On High-Dimensional Time-Variant Reliability Analysis with the Maximum Entropy Principle

The structural reliability analysis suffers from the curse of dimensionality if the associated limit state function involves a large number of inputs. This study develops a reliability analysis method that deals with high-dimensional inputs over time. The probability distribution of the structural response is reconstructed by the maximum entropy principle which is achieved by solving an optimization problem derived from the concept of relative entropy. The optimization problem is transformed into a convex one with respect to the orders of fractional moments and the Lagrange multipliers. Additionally, considering the associated computational issues, it is reformulated with side constraints on the parameters of the maximum entropy distribution. Then, a global optimization procedure is performed. The proposed method is successfully applied to the reliability analysis of a linear and a nonlinear structural system, which involves a large number of inputs deriving from the discretization of the input random processes.

MULTILEVEL QUASI-MONTE CARLO FOR INTERVAL ANALYSIS

This paper presents a multilevel quasi-Monte Carlo method for interval analysis, as a computationally efficient method for high-dimensional linear models. Interval analysis typically requires a global optimization procedure to calculate the interval bounds on the output side of a computational model. The main issue of such a procedure is that it requires numerous full-scale model evaluations. Even when simplified approaches such as the vertex method are applied, the required number of model evaluations scales combinatorially with the number of input intervals. This increase in required model evaluations is especially problematic for highly detailed numerical models containing thousands or even millions of degrees of freedom. In the context of probabilistic forward uncertainty propagation, multifidelity techniques such as multilevel quasi-Monte Carlo show great potential to reduce the computational cost. However, their translation to an interval context is not straightforward due to the fundamental differences between interval and probabilistic methods. In this work, we introduce a multilevel quasi-Monte Carlo framework. First, the input intervals are transformed to Cauchy random variables. Then, based on these Cauchy random variables, a multilevel sampling is designed. Finally, the corresponding model responses are post-processed to estimate the intervals on the output quantities with high accuracy. Two numerical examples show that the technique is very efficient for a medium to a high number of input intervals. This is in comparison with traditional propagation approaches for interval analysis and with results well within a predefined tolerance.

DIFFERENTIAL EVOLUTION ALGORITHM IN MODELS OF TECHNICAL OPTIMIZATION

At present, evolutionary optimization algorithms are increasingly used in the development of new technological processes. Evolutionary algorithms often allow the optimization procedure to be performed even in cases where classical optimization algorithms fail (e.g. gradient methods) and where an acceptable solution is sufficient to solve the optimization task. The article focuses on possibilities of using a differential evolution algorithm in the optimization process. This algorithm is often referred to in the literature as a global optimization procedure. However, we show by means of a practical example that the convergence of the classic differential algorithm to the global extreme is not generally assured and is largely dependent on the specific cost function. To remove this weakness, we designed a modified version of the differential evolution algorithm. The improved version, named the modified differential evolution algorithm, is described in the article. It is possible to prove asymptotic convergence to the global minimum of the cost function for the modified version of the algorithm.

Transferable Ion Force Fields in Water from a Simultaneous Optimization of Ion Solvation and Ion-Ion Interaction.

The poor performance of many existing nonpolarizable ion force fields is typically blamed on either the lack of explicit polarizability, the absence of charge transfer, or the use of unreduced Coulomb interactions. However, this analysis disregards the large and mostly unexplored parameter range offered by the Lennard-Jones potential. We use a global optimization procedure to develop water-model-transferable force fields for the ions K+, Na+, Cl–, and Br– in the complete parameter space of all Lennard-Jones interactions using standard mixing rules. No extra-thermodynamic assumption is necessary for the simultaneous optimization of the four ion pairs. After an optimization with respect to the experimental solvation free energy and activity, the force fields reproduce the concentration-dependent density, ionic conductivity, and dielectric constant with high accuracy. The force field is fully transferable between simple point charge/extended and transferable intermolecular potential water models. Our results show that a thermodynamically consistent force field for these ions needs only Lennard-Jones and standard Coulomb interactions.

DEGAS: differentiable efficient generator search

Network architecture search achieves state-of-the-art results in various tasks such as classification and semantic segmentation. Recently, a reinforcement learning-based approach has been proposed for generative adversarial networks (GANs) search. In this work, we propose an alternative strategy for GAN search by using a proxy task instead of common GAN training. Our method is called differentiable efficient generator search, which focuses on efficiently finding the generator in the GAN. Our search algorithm is inspired by the differential architecture search strategy and the global latent optimization procedure. This leads to both an efficient and stable GAN search. After the generator architecture is found, it can be plugged into any existing framework for GAN training. For consistency-term GAN, which we use in this work, the new model outperforms the original inception score results by 0.25 for CIFAR-10.